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| Describe days13/projects/sagenewbiew here. LINKS: http://docutils.sourceforge.net/rst.html |
= Sage Primers = |
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| Sage Tutorial | <<TableOfContents>> |
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| Goals: | '''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document. |
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| 1) Accessible to high school math teachers and undergraduate mathematics majors. | == Done / In Progress == |
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| 2) Anticipated user desires | * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] |
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| a. Content specific modules | * 1. Basics |
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| i. Quadratic Forms | * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] |
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| ii. Group theory | * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] |
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| iii. Abstract algebra | * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman |
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| iv. Calculus | * 1.4. Solving basic equations with Sage [[attachment:Ball_motion.sws]] by Jose Guzman |
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| v. Number theory | * 1.5. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]] |
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| vi. High school algebra / trigonometry / precalculus | * 2. Calculus |
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| vii. Probability | * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman |
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| viii. Statistics | * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] |
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| b. Plotting 2 and 3 dimensions | * 2.3. Integral Calculus [Sourav] |
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| c. Sage math functions (sage as calculator), sage constants | * 3. Linear Algebra |
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| d. Generate Classroom examples | * 3.1. Matrix Algebra [Sourav] |
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| i. show (), latex() | * 4. Abstract Algebra |
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| ii. matplotlab | * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer) |
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| 3) Demonstrate SAGE functionality: | * 5. Number Theory |
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| a. Primes | * 5.1. Elementary Number Theory [Erik] [[attachment:number_theory.primes_diophantine_equations.1.0.sws]] |
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| b. Random numbers | * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]] |
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| c. Plotting | * 5.7. Quaternion Algebra [Sourav] |
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| d. Interact | * 9. About this document ... |
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| e. Sage data types | |
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| f. Email(?) | |
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| 4) Programming | == To Do == |
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| a. Types, casting, relevant Sage data types | * 1. Basics |
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| b. Lists, tuples | * 1.3. Programming in Sage |
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| c. Control operators (if, then, else, logical operators, in, srange()) | * 1.5. 2D and 3D Plotting in Sage [JoseGuzman] |
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| d. Loops | * 1.6. Interact in Sage [Erik] |
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| i. For, in, srange(), range() | * 2. Calculus |
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| e. Functions | * 2.3. Multivariate Calculus |
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| f. Recursion | * 2.4. Taylor Series and Infinite Sums |
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| 5) Topics | * 2.5. Differential Equations |
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| a. Primes and factorization | * 3. Linear Algebra |
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| i. Given a random number, is it a prime? | * 3.2. Vector Spaces [Sourav] |
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| 1. Modular division | * 4. Abstract Algebra |
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| a. random() | * 4.2. Rings and Fields [Erik] |
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| b. Factor() | * 5. Number Theory |
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| 2. Euclidean algorithm | * 5.3. Cryptography [Dan] |
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| a. Recursion | * 5.4. Elliptic Curves [Aly] |
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| b. gcd() | * 5.6. Automorphic Forms |
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| 3. primality testing | * 5.8. Modular Forms |
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| a. for loops | * 6. Combinatorics |
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| b. range() | * 6.1. Counting |
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| c. is_prime() | * 6.2. Graph Theory |
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| ii. How many primes are there? | * 7. Geometry |
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| 1. prime_pi() | * 8. Statistics |
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| 2. plotting example | * 8.1. Statistical Methods [Erik] |
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| iii. Where are the primes? | * 8.2. Probability [Erik] |
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| 1. Density of primes | * 8.3. Finance |
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| 2. primes() | |
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| 3. Arithemtic sequences of primes b. Diophantine equations i. Linear Diophantine equation 1. extended euclidean algorithm 2. recursion vs iteration ii. diagonal quadratic forms; sums of squares (ENT p. 25) 1. Pythagorean triples and generating them 2. Graphing the Pythagorean triples 3. Enumerating all triples using linear intersections 4. Elliptic curves and congruent numbers (chapter 6, stein) iii. Pell’s Equation (?) |
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Sage Primers
Contents
Todo: Polish up these primers and put them in the Sage Constructions document.
Done / In Progress
0. Sage Primer Design Principles Sage Primer Design Principles.pdf primer_design_principles.rtf
- 1. Basics
1.1. Primer Template: An Example primer_template_example.sws
1.2. Sage as a Smart Calculator basics.smart_calculator_0.5.sws
1.3. Basic 2D plotting with Sage Ploting_with_Sage_v1.0.1.sws by Jose Guzman
1.4. Solving basic equations with Sage Ball_motion.sws by Jose Guzman
1.5. Sage Devel Basics [Erik, Aly] dev_for_newbies.html-this needs to be restified., development_for_newbies.sws
- 2. Calculus
2.1. Limits Calculus Analysis_tutorial_Limits_v1.0.2.sws by Jose Guzman
2.2. Differential Calculus calculus.differential_calculus_1.0.sws
- 2.3. Integral Calculus [Sourav]
- 3. Linear Algebra
- 3.1. Matrix Algebra [Sourav]
- 4. Abstract Algebra
4.1. Group Theory group_theory.sws (by Robert Beezer)
- 5. Number Theory
5.1. Elementary Number Theory [Erik] number_theory.primes_diophantine_equations.1.0.sws
5.5. Quadratic Forms quadratic_forms.sws
- 5.7. Quaternion Algebra [Sourav]
- 9. About this document ...
To Do
- 1. Basics
- 1.3. Programming in Sage
1.5. 2D and 3D Plotting in Sage [JoseGuzman]
- 1.6. Interact in Sage [Erik]
- 2. Calculus
- 2.3. Multivariate Calculus
- 2.4. Taylor Series and Infinite Sums
- 2.5. Differential Equations
- 3. Linear Algebra
- 3.2. Vector Spaces [Sourav]
- 4. Abstract Algebra
- 4.2. Rings and Fields [Erik]
- 5. Number Theory
- 5.3. Cryptography [Dan]
- 5.4. Elliptic Curves [Aly]
- 5.6. Automorphic Forms
- 5.8. Modular Forms
- 6. Combinatorics
- 6.1. Counting
- 6.2. Graph Theory
- 7. Geometry
- 8. Statistics
- 8.1. Statistical Methods [Erik]
- 8.2. Probability [Erik]
- 8.3. Finance